Electromagnetic Boundary Problems introduces the formulation and solution of Maxwell’s equations describing electromagnetism. Based on a one-semester graduate-level course taught by the authors, the text covers material parameters, equivalence principles, field and source (stream) potentials, and uniqueness, as well as:
- Provides analytical solutions of waves in regions with planar, cylindrical, spherical, and wedge boundaries
- Explores the formulation of integral equations and their analytical solutions in some simple cases
- Discusses approximation techniques for problems without exact analytical solutions
- Presents a general proof that no classical electromagnetic field can travel faster than the speed of light
- Features end-of-chapter problems that increase comprehension of key concepts and fuel additional research
Electromagnetic Boundary Problems uses generalized functions consistently to treat problems that would otherwise be more difficult, such as jump conditions, motion of wavefronts, and reflection from a moving conductor. The book offers valuable insight into how and why various formulation and solution methods do and do not work.
List of Figures
List of Tables
Preface
Author Bios
Maxwell's Equations and Sources
Maxwell Equations in Free Space
Energy Transfer and Poynting's Theorem
Macroscopic Maxwell Equations in Material Media
Multipole Expansions for Charges and Currents
Averaging of Charge and Current Densities
Conduction, Polarization, and Magnetization
Time-Harmonic Problems
Duality; Equivalence; Surface Sources
Duality and Magnetic Sources
Stream Potentials
Equivalence Principles
Jump Conditions
General Jump Conditions at a Stationary Surface
Example: Thin-Sheet Boundary Conditions
Jump Conditions at a Moving Surface
Force on Surface Sources
Example: Charge Dipole Sheet at a Dielectric Interface
Problems
Potential Representations of the Electromagnetic Field
Lorenz Potentials and their Duals (A, Φ, F, Ψ)
Hertz Vector Potentials
Jump Conditions for Hertz Potentials
Time-Harmonic Hertz Potentials
Special Hertz Potentials
Whittaker Potentials
Debye Potentials
Problems
Fundamental Properties of the Electromagnetic Field
Causality; Domain of Dependence
Domain of Dependence
Motion of Wavefronts
The Ray Equation and the Eikonal
Passivity and Uniqueness
Time-Domain Theorems
Radiation Conditions
Time-Harmonic Theorems
Equivalence Principles and Image Theory
Lorentz Reciprocity
Scattering Problems
Aperture Radiation Problems
Classical Scattering Problems
Aperture Scattering Problems
Planar Scatterers and Babinet's Principle
Problems
Radiation by Simple Sources and Structures
Point and Line Sources in Unbounded Space
Static Point Charge
Potential of a Pulsed Dipole in Free Space
Time-Harmonic Dipole
Line Sources in Unbounded Space
Alternate Representations for Point and Line Source Potentials
Time-Harmonic Line Source
Time-Harmonic Point Source
Radiation from Sources of Finite Extent; The Fraunhofer Far Field Approximation
Far Field Superposition
Far Field via Fourier Transform
The Stationary Phase Principle
Radiation in Planar Regions
The Fresnel and Paraxial Approximations; Gaussian Beams
The Fresnel Approximation
The Paraxial Approximation
Gaussian Beams
Problems
Scattering by Simple Structures
Dipole Radiation over a Half-Space
Reflected Wave in the Far Field
Transmitted Wave in the Far Field
Other Dipole Sources
Radiation and Scattering from Cylinders
Aperture Radiation
Plane Wave Scattering
Diffraction by Wedges; The Edge Condition
Formulation
The Edge Condition
Formal Solution of the Problem
The Geometrical Optics Field
The Diffracted Field
Uniform Far-Field Approximation
Spherical Harmonics
Problems
Propagation and Scattering in More Complex Regions
General Considerations
Waveguides
Parallel-Plate Waveguide: Mode Expansion
Parallel-Plate Waveguide: Fourier Expansion
Open Waveguides
Propagation in a Periodic Medium
Gel'fand's Lemma
Bloch Wave Modes and Their Properties
The Bloch Wave Expansion
Solution for the Field of a Current Sheet in Terms of Bloch Modes
Problems
Integral Equations in Scattering Problems
Green's Theorem and Green's Functions
Scalar Problems
Vector Problems
Dyadic Green's Functions
Relation to Equivalence Principle
Integral Equations for Scattering by a Perfect Conductor
Electric-Field Integral Equation (EFIE)
Magnetic-Field Integral Equation (MFIE)
Nonuniqueness and Other Difficulties
Volume Integral Equations for Scattering by a Dielectric Body
Integral Equations for Static "Scattering" by Conductors
Electrostatic Scattering
Magnetostatic Scattering
Electrostatics of a Thin Conducting Strip
Electrostatics of a Thin Conducting Circular Disk
Integral Equations for Scattering by an Aperture in a Plane
Static Aperture Problems
Electrostatic Aperture Scattering
Magnetostatic Aperture Scattering
Example: Electric Polarizability of a Circular Aperture
Problems
Approximation Methods
Recursive Perturbation Approximation
Example: Strip over a Ground Plane
Physical Optics Approximation
Operator Formalism for Approximation Methods
Example: Strip over a Ground Plane (Revisited)
Variational Approximation
The Galerkin-Ritz Method
Example: Strip over a Ground Plane (Re-Revisited)
Problems
Appendix A: Generalized Functions
Introduction
Multiplication of Generalized Functions
Fourier Transforms and Fourier Series of Generalized Functions
Multidimensional Generalized Functions
Problems
Appendix B: Special Functions
Gamma Function
Bessel Functions
Spherical Bessel Functions
Fresnel Integrals
Legendre Functions
Chebyshev Polynomials
Exponential Integrals
Polylogarithms
Problems
Appendix C: Rellich's Theorem
Appendix D: Vector Analysis
Vector Identities
Vector Differentiation in Various Coordinate Systems
Rectangular (Cartesian) Coordinates
Circular Cylindrical Coordinates
Spherical Coordinates
Poincaré's Lemma
Helmholtz’s Theorem
Generalized Leibnitz Rule
Dyadics
Problems
Appendix E: Formulation of Some Special Electromagnetic Boundary Problems
Linear Cylindrical (Wire) Antennas
Transmitting Mode
Receiving Mode
Static Problems
Electrostatic Problems
The Capacitance Problem
The Electric Polarizability Problem
Magnetostatic Problems
The Inductance Problem
The Magnetic Polarizability Problem
Problems
Index
Biography
Edward F. Kuester received a BS degree from Michigan State University, East Lansing, USA, and MS and Ph.D degrees from the University of Colorado Boulder (UCB), USA, all in electrical engineering. Since 1976, he has been with the Department of Electrical, Computer, and Energy Engineering at UCB, where he is currently a professor. He also has been a summer faculty fellow at the Jet Propulsion Laboratory, Pasadena, California, USA; visiting professor at the Technische Hogeschool, Delft, The Netherlands; invited professor at the École Polytechnique Fédérale de Lausanne, Switzerland; and visiting scientist at the National Institute of Standards and Technology (NIST), Boulder, Colorado, USA. Widely published, Dr. Kuester is a fellow of the Institute of Electrical and Electronics Engineers (IEEE), and a member of the Society for Industrial and Applied Mathematics (SIAM) and Commissions B and D of the International Union of Radio Science (URSI).
David C. Chang holds a bachelor's degree in electrical engineering from National Cheng Kung University, Tainan, Taiwan, and MS and Ph.D degrees in applied physics from Harvard University, Cambridge, Massachusetts, USA. He was previously full professor of electrical and computer engineering at the University of Colorado Boulder (UCB), USA, where he also served as chair of the department and director of the National Science Foundation Industry/University Cooperative Research Center for Microwave/Millimeter-Wave Computer-Aided Design. He then became dean of engineering and applied sciences at Arizona State University, Tempe, USA; was named president of Polytechnic University (now the New York University Polytechnic School of Engineering (NYU Poly)), Brooklyn, USA; and was appointed as NYU Poly chancellor. He retired from that position in 2013, and is now professor emeritus at the same university. Dr. Chang is a life fellow of the Institute of Electrical and Electronics Engineers (IEEE); stays active in the International Scientific Radio Union (URSI); has been named an honorary professor at five major Chinese universities; serves as chairman of the International Board of Advisors at Hong Kong Polytechnic University, Hung Hom; and was appointed special advisor to the president of Nanjing University, China.
"… a unique title by two authors whose in-depth knowledge of this material and ability to present it to others are hardly matched. While the book provides distinguishing coverage and presentation of many topics, some discussions cannot be found elsewhere. I highly recommend this outstanding piece, bringing great value as both a textbook and reference text."
—Branislav M. Notaros, Colorado State University, Fort Collins, USA"… useful for students, researchers, engineers, and teachers of electromagnetics. Today, in many universities, this discipline is taught by teachers who do not have much research experience in electromagnetism. That is why this textbook, written by world-known specialists and showing how electromagnetics courses should be built and taught, is very important. The authors have made clearer several aspects of electromagnetism which are poorly highlighted in earlier-published literature."
—Guennadi Kouzaev, Norwegian University of Science and Technology, Trondheim"Graduate students and learners of electromagnetics of any age and status: If you have not had a chance to attend graduate-level courses taught by great professors like Edward F. Kuester and David C. Chang, here comes opportunity knocking on your door. Electromagnetic Boundary Problems is borne out of course notes prepared, used, corrected, and perfected by the authors over the years at the University of Colorado, Boulder. This is a book of gems."
—IEEE Antennas and Propagation, October 2016